Tasks- "Tasks Free" or the checklist function of "ColorNote" but these are not robust enough for everyone
ClassicNote - "PalmNote" (it pulled in my Palm Desktop) or "Note Everything" which allows for file passwords
TapNote - all of the cloud storage apps on Android now have their own editors (Box, OneDrive, Google Drive, etc) and most office apps will load to most or all of the cloud storage sites
FeedReader- "Feedly"
Mileage Monitor - "aCar" but I haven't tried many
MLB Scores and NHL Score - I use the mobile sites or the official league apps my husband uses
Dr. Battery - "Battery Widget Reborn"
Internalz- "ES File Explorer" or "Astro File Manager"
A few that you haven't asked about:
MemoPad- "ColorNote" or "Keep"
Office- WPS Office (multiple panes/docs)
"Graffiti", if you really are one of us old Palm folks
"Google Opinion Survey" earn money for apps by answering brief/basic questions, usually 1-3 questions once or twice a week.
I am still looking for good replacements for some of my apps. I am down to only using my Pre+ everyday not my TP or Tungsten. I'm sorry that I can't help with more of your list.
I don't know if your phone has wireless charging but I have played with various Qi charging, what Android folks/sites say are the best, and I think they are all crap so far. If my hands didn't shake so much, I would do the TouchStone mod. I've been told that I'm too picky. I say that they don't know what inductive charging should be. I have several Qi chargers gathering dust. My touchstones are still in use. (Sorry to rant.)
Good luck.